随机分布共线微裂纹的强相互作用

微裂纹串接为宏观灾难性裂纹的过程取决于相邻微裂纹的强相互作用。微裂纹的分布规律影响材料的强度和韧性。本文研究简单的共线微裂纹构型，确定由于微裂纹长度和韧度尺寸的统计分布所产生的影响。研究结果预计了脆性材料的尺度效应，即对于相同密度的微裂纹分布，大尺寸构件的强度比小尺寸构件要低。计算还表明脆性体的强度随微裂纹分布函数标准方差的增加而减小。     

脆性材料裂纹扩展的分形运动学

大量实验结果表明脆性材料裂纹扩展路径是弯弯曲曲的，不规则的，断裂表面粗糙不平，表现出分形特征。本文应用分形几何推导出脆性材料裂纹扩展的分形运动学公式，得到了动、静态断裂韧性与分形裂纹扩展速度、裂纹长度、微结构特征量δ＿ｃ以及分形维数之间的关系；推导出了裂纹扩展速度的计算公式，得出宏观量测的裂纹扩展速度Ｖ＿０应小于分形裂纹扩展速度Ｖ；并推导出直接根据材料动、静态断裂韧性和裂纹扩展速度Ｖ＿０估算材料裂纹扩展路径的分维计算公式．本文理论分析结果与实验值在定性定量上达到了较好的一致。     

结构破坏的尺度律

文中综述了结构破坏的尺度律和尺寸效应的研究进展,尤其将重点放在准脆性材料的分析上,因为它们的尺寸效应是重要和复杂的．在回顾了尺寸效应研究的悠远发展史以后。着重讨论了三种主要类型的尺寸效应,即由于强度随机性引起的统计尺寸效应、能量释放的尺寸效应和由于微裂纹或断裂的分形特性可能引起的尺寸效应．得出了这些理论应用的明确结论．之后讨论了如何运用已知的尺寸效应律来测量材料的断裂特性,并采用内聚裂纹模型（cohesivecrackmodel）、非局域化有限元模型和离散元模型等对尺寸效应进行模化．文中还进而分析了尺寸效应在压缩失效和车相关材料行为下的有关问题,并讨论了在断裂扩展区描述含微裂纹材料所需的损伤本构关系．最后也讨论了尺寸效应对准脆性材料的多种应用,这些材料包括,如混凝土、海冰、纤维复合材料、岩石和陶瓷等．本文包含了参考文献377篇     

动态裂纹扩展中的分形效应

假设裂纹顶端沿着分形轨迹运动，建立了裂纹扩展的分形弯折（ｋｉｎｋｉｎｇ）模型来描述裂纹的动态扩展。根据这个模型，我们推导了分形裂纹扩展对劝态应力强度和裂纹速度的影响．动态应力强度因子与表观应力强度因子之比Ｋ（ｌ（ｔ），Ｖ）／Ｋ（Ｌ（ｔ），Ｏ）是表观裂纹速度Ｖ＿Ｏ，材料微结构参数（ｄ／Δａ），分维Ｄ和裂纹扩展路径的弯折角θ的函数。本文研究结果表明：在分形裂纹扩展中，表观（或量测）的裂纹速度Ｖ＿Ｏ很难接近Ｒａｙｌｅｉｇｈ波速Ｃ＿ｒ．动态断裂实验中Ｖ＿Ｏ明显低于Ｃ＿ｒ的原因可能是分形裂纹扩展效应所致。材料的微结构，裂纹扩展路径的分维和弯折角均很强地影响动态应力强度因子和裂纹扩展速度。     

非平衡统计断裂力学基础

非平衡统计断裂力学是用非平衡统计概念和方法结合微裂纹(或微空洞)演化动力学从微观机理推导出宏观力学量的断裂理论.它以微裂纹演化方程为核心,结合从微观机理求得的微裂纹长大速率和成核率以及最小强度原理,统一导出微裂纹分布函数、断裂概率、可靠性、失效率、损伤断裂动力学方程、强度、韧度和寿命等各种与断裂有关的力学量的统计分布函数、统计平均值和统计涨落.本文理论可广泛适用于金属和结构陶瓷的脆性、疲劳、延时和环境断裂等多种断裂类型.本文通过金属的脆性、疲劳和延时断裂,扼要综述了上述主要思想、方法和结果.      

动、静裂纹作用偏置效应的动焦散冲击实验

为了研究冲击荷载作用下脆性材料中运动裂纹与静止裂纹的相互作用，选取动态载荷下断裂行为与岩石材料类似且本身光学特性较好的有机玻璃（PMMA）作为实验材料，试件尺寸为220 mm×50 mm×5 mm，采用激光切割制作长度5 mm的预制裂纹和长度10 mm的静止裂纹，预制裂纹位于试件的底部边缘中心，静止裂纹的中心位于试件水平轴线。将静止裂纹偏置距离作为单一变量，采用数字激光动态焦散实验系统对含不同缺陷的PMMA进行三点弯曲实验，并结合几何分形理论研究不同偏置距离下运动裂纹的分形规律。实验结果表明:存在预制裂纹与静止裂纹的临界偏置距离（6 mm），该条件下裂纹轨迹对应的分形维数值最大，裂纹轨迹的规则程度最低，裂纹破坏形态最复杂。当预制裂纹与静止裂纹的偏置距离在0～6 mm时，裂纹Ⅰ起裂后垂直向上扩展一段距离，与静止裂纹交汇，并停滞一段时间后发生二次起裂，直至贯穿试件，偏置距离和交汇点竖向坐标值呈近似线性函数关系。偏置距离的存在不会影响裂纹Ⅰ的起裂时间和应力强度因子，但会显著减小裂纹Ⅱ的动态应力强度因子，且停滞时长随偏置距离的增大而逐渐缩短。当偏置距离大于临界偏置距离时，运动裂纹不再与静止裂纹交汇而是呈拱状向试件上边缘扩展直至贯穿，裂纹的起偏时间、起偏位置也会出现明显的滞后现象。     

冲击载荷下两裂纹间的连通规律

脆性材料内部含有大量裂纹，当某一裂纹扩展时，其他裂纹会对扩展裂纹产生影响。为了研究冲击载荷下，脆性材料内两裂纹的相互影响、连通规律及裂纹尖端应力强度因子的变化规律，利用有机玻璃板制作了含非平行双裂纹的实验试件，利用落板冲击设备进行了中低速冲击实验，结合有限元分析软件ABAQUS计算出裂纹尖端应力强度因子，利用有限差分软件AUTODYN进行了动态数值模拟研究，并将其模拟结果与实验结果进行对比分析。实验及模拟结果表明:裂纹破坏形态与AUTODYN数值模拟破坏形态基本一致；试件的断裂形态随着两裂纹间距不同而不同；裂纹间的相互影响程度随着裂纹间间距增大而减小；裂纹尖端应力强度因子K_I随着裂纹间距的增大而减小，而K_II随着裂纹间距增大而增大。     

脆性固体碎裂过程中的最快卸载特性

脆性固体在高应变率拉伸过程中常破碎为多块碎片.论文通过一个一维理论模型,研究动态脆性碎裂过程中固体内部载荷卸载规律,以及碎片尺度的计算方法.假设一维固体中裂纹等间距分布、同时起裂,研究均匀应变率拉伸作用下裂纹阵列的扩张过程.采用线弹性波动方程组描述未断裂固体的动力学关系,采用粘滞断裂模型(cohesive fracture model)描述裂纹的扩张行为,形成完整的初边值问题.采用沿特征线的有限差分计算格式求解控制方程组,得到固体在碎裂过程不同时刻下单位裂纹体内部的应力分布曲线,以及单位裂纹体平均应力随时间的变化规律,确定单位裂纹体达到完全断裂所需要的时间.在给定应变率下,分析不同裂纹间距下的碎裂卸载时间,以及使单位裂纹体以最快速度完全卸载所对应的最佳裂纹间距,并以此间距估算脆性固体在自然动态碎裂过程中的平均碎片尺度.进一步研究了具有不同粘滞性断裂特性的脆性固体的碎片尺度计算数值的差异.     

冲击载荷作用下黑砂岩动态断裂参数的分形修正

基于分形理论研究了偏折裂纹扩展路径对动载荷作用下黑砂岩的动态断裂力学参数的测试误差影响作用,采用传统的分离式霍普金森压杆（split Hopkinson pressure bar, SHPB）实验装置对修正侧开单裂纹半孔板（improved single cleavage semi-circle specimen, ISCSC）试样进行动态冲击实验,随后采用裂纹扩展计进行裂纹起裂时间与裂纹扩展速度等动态断裂力学参数测试,采用分形理论对测试的裂纹扩展速度与动态应力强度因子进行修正,利用实验-数值法对黑砂岩的动态断裂韧度进行计算。研究结果表明,ISCSC构型构件能够有效应用于岩石材料动态裂纹扩展行为的研究,并发生了止裂现象,经分形修正的裂纹扩展速度与动态断裂韧度更接近实际裂纹动态扩展情况,修正前后得到黑砂岩材料的裂纹扩展速度误差为33.51%,动态断裂韧度最大误差为7.68%,说明利用分形理论对动态断裂韧度等动态断裂参数计算更合理。     

脆性材料热-力耦合模型及热破裂数值分析方法

针对混凝土、岩石等脆性材料,利用热传导和热-力耦合的相关理论,并结合材料在细观尺度上的损伤演化规律,提出了一种考虑损伤的热-力耦合模型,并在原有材料破坏过程分析系统RFPA(Realistic Failure Process Analysis)模型的基础上建立了脆性材料热破裂过程分析的数值模拟方法.该方法考虑了脆性材料在细观层次上力学性质的非均匀性(包括强度、弹模、传导系数等),并通过统计分布函数建立了宏、细观力学性能之间的联系.对不同均匀程度材料的数值模拟结果表明:材料的非均匀性对热传导规律、热应力分布以及热破坏模式有较大的影响.材料热力学性质的非均匀性加剧了材料内部热应力分布的非均匀性,这是致使非均匀材料热破裂的一个重要因素.对稳态和瞬态热传导两种条件下的脆性介质破裂过程模拟分析表明,考虑瞬态热传导计算所得到的破裂区小于相同条件下稳态热传导所得到的结果,表明在热破裂过程分析中,应注重考虑瞬态热传导对破裂过程的影响.     

STATISTICALLY FRACTAL STRENGTH THEORY FOR BRITTLE MATERIALS

Based on the hypothesis of the fractal distribution of crack sizes in brittle materials andthe weakest link principle,the relationship between the fractal dimension of the size-frequency distri-bution of cracks and the Weibull Modulus is derived,which reveals the geometrical nature of theWeibull Modulus.The influences of the size distribution and the orientation distribution of cracks aswell as the irregularity of the crack propagation on the strength are all taken into account.Finally,ageneral expression for the statistical strength of brittle materials in complex tensile stress state is ob-tained.     

Fractal dimension evolution of microcrack net in disordered materials

Fractal geometry is used to evaluate the degree of disorder of crack size distribution in brittle damaging materials. The fractal dimension of the 2D microcrack net turns out to increase from one to two during the loading process and microcrack propagation. This means that the material becomes more disordered with the damage evolution. The longer cracks, in fact, propagate more rapidly than the shorter and, at the same time, the crack size distribution increases its statistical dispersion. Some numerical examples, related to different initial microcrack densities and size distributions, are illustrated with the computer simulation of the system evolution.     

Modeling dynamic brittle behavior of materials with circular flaws or pores

Compressive failure of brittle materials is driven primarily by crack growth from pre-existing flaws in the material. These flaws, such as grain boundaries, pores, preexisting cracks, inclusions and missing grains, are randomly spaced and have a range of possible shapes and sizes. The current work proposes a micromechanics-based model for compressive dynamic failure of brittle materials with circular pore flaws, which incorporates both the number density and the size distribution of flaws. Results show that the distribution of flaw sizes is very important, particularly at moderate strain rate, since analyses based solely on the mean flaw size overpredict strength. Therefore, in order to increase dynamic strength at low to moderate strain rates, it is most effective to control the presence of large flaws. At very high strain rates, however, crack growth is activated even in small flaws and therefore controlling the total number density rather than the size of the flaws is effective for increasing dynamic strength. Finally, the model shows that neglecting very small flaws in the pore population may not have significant effects on the results in many cases, suggesting that the model is a useful tool for identifying a minimum resolution required for experimental characterization of microstructure.     

The brittle fracture criterion based on the maximum tensile stress on the surface of blunt crack tip

The brittle fracture criterion is developed for a blunted crack. The curvature radius of the blunt crack tip is suggested as a characteristic length for brittle materials, and then the fracture toughness of the brittle materials can be determined from the cohesion strength and the characteristic length of the materials.     

Fractal geometry concerned with stable and dynamic fracture mechanics

Fractal modeling of the rugged crack geometry is considered for the stable and dynamic fracture mechanics characterizing the morphology of a fracture surface and the influence of its growth. It is shown that the fractal dimension has a strong influence on the rising of the R-curve in brittle materials. For the unstable Griffith–Mott’s approach or dynamical crack growth the fractal dimension has a strong influence on the velocity limit of the crack growth. It is also shown that the limit of crack velocity lowers with increasing surface ruggedness (higher fractal dimension D = 2 − H) explaining the intangibility of the Rayleigh wave velocity by the cracks.     

Comparison of the statistics of two fracture modes

T strengths of an aggregate material are calculated for the following two modes of fracture: (i) by independent fracture of individual volume elements separated by a crack propagation barrier, (ii) by propagation of a crack from the weakest volume element in the absence of a propagation barrier. The first case is analysed by means of a model which consists of an assembly of layers in series, each layer representing a bundle of volume elements uniformly loaded in parallel. The strength distribution of the stacked layers is obtained by an application of the statistical theory of bundles of filaments after Daniels and others, and ‘weakest link’ statistics are used to yield the strength distribution of the cylindrical bodies. For comparison, the ‘weakest link’ statistics of Epstein and others are given for the second case which corresponds to the usual cleavage fracture model of brittle materials. The expected volume and shape effects of the two modes are compared.     

脆性断裂的微观机理和非平衡统计特性

Ⅰ.引言如何才能将断裂的微观机理与宏观特性结合起来,把断裂理论建立于微裂纹演化的微观动力学基础上,从而统一导出所有重要的宏观力学量并以某些更基本的物理量表示之?这是人们为实现材料的强度和韧性设计必需解决的一个重要理论课题。就脆性断裂来说,尽管现有几个主要代表性的理论如断裂力学理论、位错理论和统计理论都各取得一定成就,但就其理论框架来说,由于明显的局限性,却难以发展成可供指导设计的理论。因此,人们在探索微观与宏观相结合的断裂理论。最近的工作表明:从微裂纹演      

Balancing strength and toughness of calcium-silicate-hydrate via random nanovoids and particle inclusions: Atomistic modeling and statistical analysis

As the most widely used manufactured material on Earth, concrete poses serious societal and environmental concerns which call for innovative strategies to develop greener concrete with improved strength and toughness, properties that are exclusive in man-made materials. Herein, we focus on calcium silicate hydrate (C-S-H), the major binding phase of all Portland cement concretes, and study how engineering its nanovoids and portlandite particle inclusions can impart a balance of strength, toughness and stiffness. By performing an extensive +600 molecular dynamics simulations coupled with statistical analysis tools, our results provide new evidence of ductile fracture mechanisms in C-S-H – reminiscent of crystalline alloys and ductile metals – decoding the interplay between the crack growth, nanovoid/particle inclusions, and stoichiometry, which dictates the crystalline versus amorphous nature of the underlying matrix. We found that introduction of voids and portlandite particles can significantly increase toughness and ductility, specially in C-S-H with more amorphous matrices, mainly owing to competing mechanisms of crack deflection, voids coalescence, internal necking, accommodation, and geometry alteration of individual voids/particles, which together regulate toughness versus strength. Furthermore, utilizing a comprehensive global sensitivity analysis on random configuration-property relations, we show that the mean diameter of voids/particles is the most critical statistical parameter influencing the mechanical properties of C-S-H, irrespective of stoichiometry or crystalline or amorphous nature of the matrix. This study provides new fundamental insights, design guidelines, and de novo strategies to turn the brittle C-S-H into a ductile material, impacting modern engineering of strong and tough concrete infrastructures and potentially other complex brittle materials.